Journal Club
`Mathematics and the Bucky Ball', Sternberg and Chung, American Scientist 81 (1993) 56.
Berichter: Robert MacKay

27th May 1993

Brian Buck Oxford
"Sunspots, with application to time series analysis''
ABSTRACT: Astrophysical literature contains many attempts to extract clues to the physics of the sun from the large database of Wolf Sunspot Numbers; in particular, an irregular cycle of eleven years has been known for a long time. Most of the techniques of time series analysis have been used on this data set in recent years. I have selected this interesting record as a test bed for developing new methods of spectral analysis and I will explain how the problem of identifying periodicities in a short time series can be treated by Bayesian probability theory and the method of Maximum Entropy. The fine structure of the derived sunspot spectrum shows some intriguing features.

8th June 1993

David Rand Warwick
"Evolution and ecology in spatially extended systems''

"Can we tune the superconductor-insulator transition with magnetic impurities

26/10/1995

Mike Godfrey, Manchester

"SIC DFT of bandgap renormalisation

2/11/1995

Mark Hindmarsh, Sussex

"Formation of topological defects

9/11/1995

Mark Hadley, Warwick

"Is there an alternative to quantum gravity?"

16/11/1995

Paul Bressloff, GEC

"Self-organising neural networks near the AI limit

23/11/1995

Keith Moffat, Cambridge

"Magnetohydrodynamics of planets, stars and galaxies"

30/11/1995

Tim Sluckin, Southampton

"Liquid Crystals at Surfaces"

25/01/1996

Mike Kearney, Loughborough

"Drift, diffusion and non-linear propagation on tree structures"

01/02/1996

Volker Heine, Cambridge

"The floppy/stiff duality and mechanism for structural phase transitions in silicate framework structures"
Silicate framework structures consist of rather stiff units (tetrahedra and octahedra) rather loosely jointed at their corners by shared oxygen atoms. Rigid Unit Modes are special phonons which are geometrically allowed possible motions while units remain completely rigid. They provide pathways for soft mode phase transitions and also have wider application to fluctuations, atomic ordering, the theory of the transition temperature, pressure effects, negative coefficient of expansion, and adsorption sites in zeolites.

"High pressure electronic structure and phase transitions of iron compounds and the nature of the earth's core"

13/06/1996

Journal Club, Warwick

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10/10/1996

Miron Amusia, Imperial College

"Atoms as multi-particle systems"

17/10/1996

Robin Ball, Cavendish

"Mechanisms for global optimization of river networks from local erosion rules"

24/10/1996

Nick Hill, Leeds

"From the microscopic to the macroscopic: pattern formation by suspensions of swimming micro-organisms"

31/10/1996

David Lowe, Aston

"From financial markets to the research assessment exercise: Some recent developments in the application of artificial neural networks"

07/11/1996

Alexei Tsvelik, Oxford

"Luttinger and Fermi liquids: stability with respect to interchain hopping"

14/11/1996

George Japaridze, Sussex

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21/11/1996

Richard Dendy, Culham

"Fusion product transport in strongly turbulent plasmas"

28/11/1996

Andrew King, Birmingham

"Some unsteady free-surface flows"

05/12/1996

Stephen Julian, Cavendish

"Strongly correlated electrons in the T 0 limit: heavy fermions and other exotica"

16/01/1997

Andrew Steane, Clarendon

"Stabilising quantum behaviour by quantum error correction"

23/01/1997

James Nicholls, Cavendish

"Electron-electron interactions in 1 and 2 dimensions as observed in GaAs systems"

30/01/1997

Frank Hekking, Cavendish

"Quantum fluctuations in the equilibrium state of a thin superconducting loop"

06/02/1997

Frank Pinski, Warwick

"The electronic structure and phase diagrams of alloys"

13/02/1997

Matthew Turner, Warwick

"Polymers, BSE and CJD"

20/02/1997

Eric Blackman, Cambridge

"Aspects of dynamo theory and the 'backreaction' problem"

27/02/1997

Tom McLeish, Leeds

"On the trail of topological fluids"

06/03/1997

Steve Hayden, Bristol

"The de Haas van Alphen effect in the mixed state of superconductors"
The de Haas-van Alpen effect (Landau quantum oscillations) has now been reported in a number of type II superconductors, including NbSe2, Nb3Sn, V3Si, CeRu2 and the borocarbides. This technique is potentially a powerful probe of the superconducting state. I will discuss the present experimental situation, compare observations with a number of theoretical models in the literature and suggest future directions for this work.

This seminar is being held together with the CSC seminar series at 3 p.m. Meeting point: Mathematics Common Room 3:00 p.m., starting with tea. Talks are at 3:10 pm in room B3.03 of the Mathematics Institute.

Second-order phase transitions are classified according to the values of critical exponents. In the 1960^Òs, four famous scaling relations linking these exponents were discovered and these are of fundamental importance in statistical physics and related areas. In certain important circumstances the transitional behaviour is modified by so-called logarithmic corrections. These are subtle effects that cloud the leading terms, and characterize the system. Here it shown that these logarithmic terms are also inter-related, just as the leading terms are, and a set of new scaling relations for them is presented. Consequently, a long-standing debate is automatically resolved. This concerns the Ising model in two dimensions, an old favourite for statistical physicists. Adding disorder to this system changes its critical behaviour but the precise nature of these changes has been under question. The new scaling relations relate hitherto elusive exponents characterizing these changes to well established ones in an unambiguous and precise fashion. This is one demonstration of how the new scaling relations are expected to become an important tool in modern statistical mechanics.

I will present an efficient first-principles approach to calculate Fermi surface averages and spectral properties of solids, and use it to compute the anomalous Hall conductivity and magneto-optical absorption of iron. The method works by mapping the low-energy electronic structure onto a set of maximally-localised, partially occupied Wannier functions. In this way we can calculate Brillouin zone averages at ab-initio accuracy with only tight-binding cost.

Thu 8 Feb '07

Ard Louis, Oxford
Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales

We describe in detail how to implement a coarse-grained hybrid Molecular Dynamics and Stochastic Rotation Dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length-scales of this problem is emphasised[1,2]. Applications to be discussed include: The effect of hydrodynamics and Brownian fluctuations on percolation and aggregation, the sedimentation of colloidal particles, dynamic lane formation in driven suspensions, and the direct simulation of a microfluidic nano-pump. [1] Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales, J.T. Padding and A.A. Louis, Phys. Rev. E 74, 031402 (2006) [2] Hydrodynamic and Brownian Fluctuations in Sedimenting Suspensions J.T. Padding and A. A. Louis, Phys. Rev. Lett. 93, 220601 (2004)

Recent angle-resolved photoemission spectroscopy (ARPES) has identified that a finite-range Fröhlich electron-phonon interaction (EPI) with c-axis polarized optical phonons is important in cuprate superconductors. Thus, it is interesting to determine what sorts of phonon-mediated unconventional pairing are possible. To this end, schemes that can cope beyond the limited range of applicability for BCS theory need to be developed. In this talk, I describe results from two major extensions: A high-order weak-coupling expansion (extended Eliashberg theory) and an advanced continuous-time quantum Monte-Carlo algorithm (CTQMC). I first demonstrate how expanding the electron self-energy to second order in the binding energy leads to the conclusion that d-wave superconductivity can be mediated by phonons, with Coulomb repulsion stabilising d- over s- wave pairing [1]. Eliashberg theories may be used for moderate electron-phonon couplings, however, to determine exact results at intermediate to strong couplings we use a CTQMC algorithm that we recently developed for studying bipolarons (two electrons bound by phonons). The CTQMC algorithm is excellent for investigating unconventional pairing possibilities. We have investigated the effective mass and binding energies of singlet and triplet real-space bipolarons on a number of lattice types [2,3]. We demonstrate that bipolarons can be simultaneously small and light, provided that suitable conditions on the electron-phonon and electron-electron interaction and lattice type are satisfied. Such light small bipolarons are a necessary precursor to high-temperature Bose-Einstein Condensation (BEC) in solids. The light bipolaron mass is shown to be universal in systems made of triangular plaquettes, due to a novel crab-like motion. We discuss the conditions under which such particles may form a BEC with an exceptionally high transition temperature [2].

Thu 1 March '07

Joerg Wunderlich, Hitachi/Cavendish
Extraordinary magnetoresistance effects and local control of magnetocrystalline anisotropy in (Ga,Mn)As devices

The family of (III,Mn)V ferromagnetic semiconductors offers unique opportunities for exploring the integration of two frontier areas in information technology: spintronics and nano-electronics. In my talk I will address two novel phenomena recently observed in micro- and nano-structures patterned from this ferromagnetic material with strong spin-orbit coupling, the Coulomb blockade Anisotropic Magnetoresistance effect and lithographically controlled magnetocrystalline anisotropy applied for current induced spin- transfer-torque domain wall propagation.

Half-metallic materials, which exhibit complete spin-polarisation at the Fermi level, hold great promise for device applications in the field of spintronics. Amongst a variety of drawbacks, however, one of the most pressing is a lack of knowledge concerning surface and interface properties. In particular, the relationship between the stability of different surface/interface phases and the presence of surface/interface localised electronic states is of great importance. In this talk, I will describe density functional calculations aimed at elucidating this relationship for various surfaces of the half-metallic semi-Heusler alloy NiMnSb and the half-metallic zincblende phase of MnSb.

Marshall Stoneham, UCL
Dynamics at the Nanoscale: Making sense of scent

Even in 1900, a few leading scientists doubted atoms existed, despite the new chemical industry underpinned by atomistic ideas. In 1970, some leading figures in electronics still claimed they had no need to believe in electrons, despite the new microelectronics. Today, we readily accept that matter is quantised (atoms), as is charge (electrons). Yet many are still reluctant to see a role for the quantum phenomena recognised in Planck's constant. But when physical sciences address the nanoscale, there is no way to avoid such quantum phenomena. Even for the biosciences, it is clear that nature must exploit quantum behaviour even at ambient temperatures. One striking result is that you probably have a quantum sensor in your nose.

Ben Simons, Cavendish
Theory of epidermal maintenance: of mice and men

One of the main challenges in biology is to understand how stem cells and their progeny function to maintain adult tissue. Recent developments in genetic labelling provide access to a wealth of clone fate data at single cell resolution over time scales long enough to address reliably the kinetics of cell fate in mouse epidermis. Drawing on these results, we show that epidermal maintenance conforms to a remarkably simple dynamics involving a critical (Galton-Watson) birth-death process, overturning a paradigm long-held in the scientific literature. Motivated by these findings, we argue that the mouse model can be straightforwardly incorporated into a generalised theory which provides a role for a quiescent stem cell population, and identifies the mechanism of pattern formation seen in human epidermis as an arrested spinodal decomposition. We discuss the implications of these results on the general mechanism of tissue maintenance, repair, and tumour formation.

CeCoIn5 may well be the drosophilia for correlated electron physics. This heavy fermion superconductor sits on the border of antiferromagnetism, is a d-wave superconductor, and possibly exhibits a novel inhomogeneous superconducting state in high magnetic fields. NMR measurements have revealed a subtle interplay of antiferromagnetism and superconductivity in this system, and may lead to a new paradigm for quantum critical phenomena in Kondo lattices.